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Polish second paragraphs of noise model subsecions

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Andreas Tsouchlos
2026-04-28 18:12:21 +02:00
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src/thesis/chapters/3_fault_tolerant_qec.tex
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@@ -178,9 +178,10 @@ We visualize the different types of noise models in
The simplest type of noise model is \emph{bit-flip} noise. The simplest type of noise model is \emph{bit-flip} noise.
This corresponds to the classical \ac{bsc}, i.e., only $X$ errors on the This corresponds to the classical \ac{bsc}, i.e., only $X$ errors on the
data qubits are possible \cite[Appendix~A]{gidney_new_2023}. data qubits are possible \cite[Appendix~A]{gidney_new_2023}.
This type of noise model is shown in \autoref{subfig:bit_flip}.
Note that we cannot use bit-flip noise to develop fault-tolerant Note that we cannot use bit-flip noise to develop fault-tolerant
systems, as it doesnt't account for errors during the syndrome extraction. systems, as it doesnt't account for errors during the syndrome extraction.
This type of noise model is shown in \autoref{subfig:bit_flip}.
%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%
\subsection{Depolarizing Channel} \subsection{Depolarizing Channel}
@@ -193,12 +194,12 @@ errors, we obtain the \emph{depolarizing channel}
It is well-suited for modeling memory experiments, where data qubits It is well-suited for modeling memory experiments, where data qubits
are stored idly for some period of time and errors accumulate due to are stored idly for some period of time and errors accumulate due to
decoherence. decoherence.
Bit-flip noise and the depolarizing channel are sometimes referred to
as \emph{code capacity noise models}.
While the depolarizing channel is still not suited for the design and While the depolarizing channel is still not suited for the design and
simulation of fault-tolerant systems, it is already complex enough to simulation of fault-tolerant systems, it is already complex enough to
be used to gauge the suitability of a code for the \ac{qec} problem. be used to gauge the suitability of a code for the \ac{qec} problem.
Bit-flip noise and the depolarizing channel are sometimes referred to
as \emph{code capacity noise models}.
%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%
\subsection{Phenomenological Noise} \subsection{Phenomenological Noise}
@@ -210,17 +211,18 @@ Here, we consider multiple rounds of syndrome measurements with a
depolarizing channel before each round. depolarizing channel before each round.
Additionally, we allow for measurement errors by having $X$ error Additionally, we allow for measurement errors by having $X$ error
locations right before each measurement \cite[Appendix~A]{gidney_new_2023}. locations right before each measurement \cite[Appendix~A]{gidney_new_2023}.
Note that it is enough to only consider $X$ errors at this point, Note that it is enough to only consider $X$ errors at these points,
since that is the only type of error directly affecting the since that is the only type of error directly affecting the
measurement outcomes. measurement outcomes.
This model is depicted in \autoref{subfig:phenomenological}. This model is depicted in \autoref{subfig:phenomenological}.
While not fully capturing all possible error mechanisms, While not fully capturing all possible error mechanisms,
phenomenological noise is already \ldots . phenomenological noise is already a significant step beyond the code
Additionally, there are applications were the consideration of capacity noise models.
phenomenological noise is enough. Additionally, there are applications where the
It can, for example, be used for \ldots \red{the design of consideration of phenomenological noise is enough.
fault-tolerant circuitry} \cite[Sec.~4.2]{derks_designing_2025}. It can, for example, be used for guiding the design of fault-tolerant
circuitry [DTTBE25, Sec. 4.2].
%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%
\subsection{Circuit-Level Noise} \subsection{Circuit-Level Noise}
@@ -238,6 +240,9 @@ This type of noise model is shown in \autoref{subfig:circuit_level}.
While phenomenological noise is useful for some design aspects of While phenomenological noise is useful for some design aspects of
fault tolerant circuitry, for simulations, circuit-level noise should fault tolerant circuitry, for simulations, circuit-level noise should
always be used \cite[Sec.~4.2]{derks_designing_2025}. always be used \cite[Sec.~4.2]{derks_designing_2025}.
Note that this introduces new challenges during the decoding process,
as the decoding complexity is increased considerably due to the many
error locations.
\begin{figure}[t] \begin{figure}[t]
\centering \centering